SET® Mathematics
Proof of Theorem 1.4

a(a * b) = b

Two cases exist: a = b or ab   Case 1: If a = b then 1(1*1) = 1 1*1 = 1 1 = 1 Case 2: If ab then 1(1*2)=2 1*3=2 2=2 Note: This is just a case that a set of three cards can be made by taking any two of the three cards a*b=c means b=c*a means a=b*c, now we see that (a*b)=a*b, then move to the other side... a(a*b)=b